Abstract
In this chapter, we have discussed two types of widely used mathematical models, the linear model and the dynamic system model. The linear model and the dynamic system model (often formulated in a specific form called the state-space model) are two distinct types of mathematical structures, both with popular applications in many disciplines of engineering. These two types of the models have very different mathematical properties and computational structures. Instead of using a high-dimensional linear model to represent the temporal correlation structure of a signal, a low-dimensional dynamic system model can be used for efficient computations.
Keywords
- Vocal Tract
- Dynamic System Model
- Linear Prediction Coefficient
- Hide Markov Model State
- Discrete Hide Markov Model
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Rabiner LR, Juang BH (1993) Fundamentals of speech recognition. Prentice-Hall of India, New Delhi
Hansen J, Proakis J (2000) Discrete-time processing of speech signals, 2nd edn. IEEE Press, New York
Mammone R, Zhang X, Ramachandran R (1996) Robust speaker recognition: a feature based approach. IEEE Signal Process Mag 13:58–71
Gudnason J (2007) Voice source cepstrum processing for speaker identification. Ph.D. thesis, University of London
Dunn HK (1961) Methods of measuring vowel formant bandwidths. J Acoust Soc Am 33(12):1737–1746
Fant G (1960) Acoustic theory of speech production. Mouton, The Hague
Miller RL (1959) Nature of the vocal chord wave. J Acoust Soc Am 31:667–677
Wong DY, Markel JD, Gray AH (1979) Glottal inverse filtering from the acoustic speech waveform. IEEE Trans Acoust Speech Signal Process 27(4):350–355
Quatieri TF (2004) Discrete-time speech signal processing, principles and practice. Pearson Education, Upper Saddle river
Rabiner LR, Shafer RW (1989) Digital signal processing of speech signals. Prentice-Hall, Englewood Cliffs
Gold B, Morgan N (2002) Speech and audio signal processing. Wiley, New York
Makhoul J (1975) Linear prediction: a tutorial review. In. Proceedings of the IEEE, vol 64, pp 561–580
Atal BS (1974) Effectiveness of linear prediction characteristics of the speech wave for automatic speaker identification and verification. J Acoust Soc Am 55:1304–1312
Teager HM (1980) Some observations on oral air flow during phonation. IEEE Trans Speech Audio Process 28(5):599–601
Campbell J (1997) Speaker recognition: a tutorial. Proc IEEE 511(9):1437–1462
Honda K (2008) Physiological processes of speech production. Springer, Berlin
Hermansky H (1990) Perceptual linear prediction analysis for speech. J Acoust Soc Am 87:1738–1752
Rosenberg AE, Sambur MR (1975) New techniques for automatic speaker verification. IEEE Trans Acoust Speech Signal Process 23(2):169–176
Deng L, O’Shaughnessy D (2003) Speech processing a dynamic and optimization-oriented approach. Marcel Dekker, New York
Tanizaki H (1996) Nonlinear filters—estimation and applications, 2nd edn. Springer, Berlin
Ghahramani Z, Roweis S (1999) Learning nonlinear dynamic systems using an em algorithm. Adv Neural Inf Process Syst 11:1–7
Segall A (1976) Stochastic processes in estimation theory. IEEE Trans Inf Theory IT-22:275–286
Tong H (1990) Non-linear time series—a dynamical system approach. Oxford University Press, Oxford
Papoulis A (1984) Probability, random variables and stochastic processes. McGraw-Hill, New York
Kantner M (1979) Lower bounds for nonlinear prediction error in moving avarage processes. Ann Prob 7(1):128–138
Casdagli M, jardins D, Eubank S, Farmer JD, Gibson J, Theiler J, Hunter N (1992) Nonlinear modeling of chaotic time series: theory and applications. In: Kim J, Stringer J (eds) Applied chaos. Wiley, New York, pp 335–380
Farmer JD, Sidorowich JJ (1988) Exploiting chaos to predict the future and reduce noise. In: Lee YC (ed) Evolution, learning, and cognition. World Scientific, Singapore, pp 277–330
Sicuranza GL (1992) Quadratic filters for signal processing. In: Proceedings of IEEE, vol 80, pp 1263–1285
Thyssen J, Nielsen H, Hansen SD (1994) Non-linear short term prediction in speech coding. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing (ICASSP’94), Adelaide, pp I-185–I-188
Singer AC, Wornell GW, Oppenheim AV (1994) Nonlinear autoregressive modeling and estimation in the presence of noise. Dig Signal Process 4:207–221
Priestley MB (1988) Non-linear and non-stationary time series analysis. Academic Press, London
Birgmeier M (1995) A fully kalman-trained radial basis function network for nonlinear speech modeling. In: Proceedings of IEEE international conference on neural networks, (ICNN’95), Perth
Birgmeier M (1996) Nonlinear prediction of speech signals using radial basis function networks. In: EUSIPCO’96, vol 1, pp 459–462
de Maria FD, Figueiras AR (1995) Radial basis functions for nonlinear prediction of speech in analysis-by-synthesis coders. In: Proceedings of IEEE workshop on nonlinear signal and image processing, Halkidiki
Lapedes A, Farber R (1998) How neural nets work. In: Lee YC (ed) Evolution, learning, and cognition. World Scientific, Singapore, pp 231–346
Tishby N (1990) A dynamical systems approach to speech processing. In: Proceedings of IEEE international conference on acoustics, speech, and, signal processing (ICASSP’90)
Wu L, Niranjan M, Fallside F (1994) Fully vector quantized neural network-based code-excited nonlinear predictive speech coding. IEEE Trans Speech Audio Process 2(4):482–489
Haykin S, Li L (1995) Nonlinear adaptive perdiction of nonstationary signals. Signal Process 43:526–535
Wu L, Niranjan M (1994) On the design of nonlinear speech predictors with recurrent nets. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing (ICASSP’94), Adelaide, pp II-529–II-532
Lorenz EN (1969) Atmospheric predictability as revealed by naturally occurring analogues. J Atmos Sci 26:636–646
Bogner RE, Li T (1989) Pattern search prediction of speech. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing (ICASSP’89), Glasgow, pp 180–183
Yakowitz S (1987) Nearest neighbor methods for time series analysis. J Time Ser Anal 8(2):235–247
Gersho A (1989) Optimal nonlinear interpolative vector quantization. IEEE Trans Comm 38(9):1285–1287
Lee Y, Johnson D (1993) Nonparametric prediction of non-gaussian time series. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing (ICASSP’93), Minneapolis, MN, pp IV-480–IV-483
Rao BLSP (1983) Nonparametric functional estimation. Academic Press, Orlando
Kubin G (1995) Nonlinear processing of speech. In: Kleijn WB, Paliwal KK (eds) Speech coding and synthesis. Elsevier Science, Amsterdam
Bishop C (1997) Neural networks for pattern recognition. Clarendon Press, Oxford
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Holambe, R.S., Deshpande, M.S. (2012). Linear and Dynamic System Model. In: Advances in Non-Linear Modeling for Speech Processing. SpringerBriefs in Electrical and Computer Engineering(). Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1505-3_3
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